Higher Order Singular Value Decomposition Research Articles

Data repairing and resolution enhancement using data-driven modal decomposition and deep learning

This paper introduces a new series of methods which combine modal decomposition algorithms, such as singular value decomposition and high-order singular value decomposition, and deep learning architectures to repair, enhance, and increase the quality and precision of numerical and experimental data. A combination of two- and three-dimensional, numerical and experimental dasasets are used to demonstrate the reconstruction capacity of the presented methods, showing that these methods can be used to reconstruct any type of dataset, showing outstanding results when applied to highly complex data, which is noisy. The combination of benefits of these techniques results in a series of data-driven methods which are capable of repairing and/or enhancing the resolution of a dataset by identifying the underlying physics that define the data, which is incomplete or under-resolved, filtering any existing noise. These methods and the Python codes are included in the first release of ModelFLOWs-app.11The website of the software is available at https://modelflows.github.io/modelflowsapp/.

Qubits as hypermatrices and entanglement

In this paper, we represent n-qubits as hypermatrices and consider various applications to quantum entanglement. In particular, we use the higher-order singular value decomposition of hypermatrices to prove that the π-transpose is an LU invariant. Additionally, through our construction we show that the matrix representation of the combinatorial hyperdeterminant of 2n-qubits can be expressed as a product of the second Pauli matrix, allowing us to derive a formula for the combinatorial hyperdeterminant of 2n-qubits in terms of the n-tangle.

Adaptive higher-order singular value decomposition clutter filter for ultrafast Doppler imaging of coronary flow under non-negligible tissue motion

Background and Objective:With the development of advanced clutter-filtering techniques by singular value decomposition (SVD) and leveraging favorable acquisition settings such as open-chest imaging by a linear high-frequency probe and plane waves, several studies have shown the feasibility of cardiac flow measurements during the entire cardiac cycle, ranging from coronary flow to myocardial perfusion. When applying these techniques in a routine clinical setting, using transthoracic ultrasound imaging, new challenges emerge. Firstly, a smaller aperture is needed that can fit between ribs. Consequently, diverging waves are employed instead of plane waves to achieve an adequate field of view. Secondly, to ensure imaging at a larger depth, the maximum pulse repetition frequency has to be reduced. Lastly, in comparison to the open-chest scenario, tissue motion induced by the heartbeat is significantly stronger. The latter complicates substantially the distinction between clutter and blood signals. Methods:This study investigates a strategy to overcome these challenges by diverging wave imaging with an optimal number of tilt angles, in combination with dedicated clutter-filtering techniques. In particular, a novel, adaptive, higher-order SVD (HOSVD) clutter filter, which utilizes spatial, temporal, and angular information of the received ultrasound signals, is proposed to enhance clutter and blood separation. Results:When non-negligible tissue motion is present, using fewer tilt angles not only reduces the decorrelation between the received waveforms but also allows for collecting more temporal samples at a given ensemble duration, contributing to improved Doppler performance. The addition of a third angular dimension enables the application of HOSVD, providing greater flexibility in selecting blood separation thresholds from a 3-D tensor. This differs from the conventional threshold selection method in a 2-D spatiotemporal space using SVD. Exhaustive threshold search has shown a significant improvement in Contrast and Contrast-to-Noise ratio for Power Doppler images filtered with HOSVD compared to the SVD-based clutter filter. Conclusion:With the improved settings, the obtained Power Doppler images show the feasibility of measuring coronary flow under the influence of non-negligible tissue motion in both in vitro and ex vivo.

Underdetermined blind source separation based on third‐order cumulant and tensor compression

AbstractA method for Underdetermined Blind Source Separation is proposed using third‐order cumulants and tensor compression. To effectively suppress symmetrical distributed noise, the third‐order cumulant is considered. Additionally, the complexity of high‐dimensional tensors can be reduced through high order singular value decomposition (HOSVD) for compression purposes. The method begins by calculating the third‐order cumulant tensor for whitening signals at different time delays, and then stacks several cumulants into a fourth‐order tensor. The HOSVD decomposition is applied to the fourth‐order tensor, compressing the high‐dimensional tensor into a low‐dimensional core tensor. Next, the core tensor is further decomposed using the canonical polyadic decomposition, and the resulting factor matrices are fused to obtain an estimation of the mixed matrix. Finally, leveraging the signal independence, a matrix diagonalisation method is employed to recover the source signals. Theoretical analysis and simulation results demonstrate that the proposed method effectively suppresses the influence of Gaussian noise, reduces computational complexity, and saves computational time. Moreover, compared with five representative approaches, the proposed method achieves superior separation results. Specifically, for the 3 × 4 mixed model with a signal‐to‐noise ratio of 20 dB, the average relative error of speech signal and radio signal are −11.02 and −6.8 dB respectively.

Randomized two-sided subspace iteration for low-rank matrix and tensor decomposition

The low-rank approximation of big data matrices and tensors plays a pivotal role in many modern applications. Although, a truncated version of the singular value decomposition (SVD) furnishes the best approximation, its computation is challenging on modern, multicore architectures. Recently, the randomized subspace iteration has shown to be a powerful tool in approximating large-scale matrices. In this paper we present a two-sided variant of the randomized subspace iteration. Novel in our work is the exploitation of the unpivoted QR factorization, rather than the SVD, for factorizing the compressed matrix. Hence our algorithm is a randomized rank-revealing URV decomposition. We prove the rank-revealingness of our algorithm by establishing bounds for the singular values as well as the other blocks of the compressed matrix. We further provide bounds on the error of the low-rank approximations of the proposed algorithm, in both 2- and Frobenius norm. In addition, we employ the proposed algorithm to efficiently compute low rank tensor decompositions: we present two randomized algorithms, one for the truncated higher-order SVD, and the other for the tensor SVD. We conduct numerical tests on (i) various classes of matrices, and (ii) synthetic tensors and real datasets to demonstrate the efficacy of the proposed algorithms.

Adaptive Tensor-Based Feature Extraction for Pupil Segmentation in Cataract Surgery.

Cataract surgery remains the only definitive treatment for visually significant cataracts, which are a major cause of preventable blindness worldwide. Successful performance of cataract surgery relies on stable dilation of the pupil. Automated pupil segmentation from surgical videos can assist surgeons in detecting risk factors for pupillary instability prior to the development of surgical complications. However, surgical illumination variations, surgical instrument obstruction, and lens material hydration during cataract surgery can limit pupil segmentation accuracy. To address these problems, we propose a novel method named adaptive wavelet tensor feature extraction (AWTFE). AWTFE is designed to enhance the accuracy of deep learning-powered pupil recognition systems. First, we represent the correlations among spatial information, color channels, and wavelet subbands by constructing a third-order tensor. We then utilize higher-order singular value decomposition to eliminate redundant information adaptively and estimate pupil feature information. We evaluated the proposed method by conducting experiments with state-of-the-art deep learning segmentation models on our BigCat dataset consisting of 5,700 annotated intraoperative images from 190 cataract surgeries and a public CaDIS dataset. The experimental results reveal that the AWTFE method effectively identifies features relevant to the pupil region and improved the overall performance of segmentation models by up to 2.26% (BigCat) and 3.31% (CaDIS). Incorporation of the AWTFE method led to statistically significant improvements in segmentation performance (P < 1.29 × 10-10 for each model) and yielded the highest-performing model overall (Dice coefficients of 94.74% and 96.71% for the BigCat and CaDIS datasets, respectively). In performance comparisons, the AWTFE consistently outperformed other feature extraction methods in enhancing model performance. In addition, the proposed AWTFE method significantly improved pupil recognition performance by up to 2.87% in particularly challenging phases of cataract surgery.

A DEIM Tucker tensor cross algorithm and its application to dynamical low-rank approximation

We introduce a Tucker tensor cross approximation method that constructs a low-rank representation of a d-dimensional tensor by sparsely sampling its fibers. These fibers are selected using the discrete empirical interpolation method (DEIM). Our proposed algorithm is referred to as DEIM fiber sampling (DEIM-FS). For a rank-r approximation of an O(Nd) tensor, DEIM-FS requires access to only dNrd−1 tensor entries, a requirement that scales linearly with the tensor size along each mode. We demonstrate that DEIM-FS achieves an approximation accuracy close to the Tucker-tensor approximation obtained via higher-order singular value decomposition at a significantly reduced cost. We also present DEIM-FS (iterative) that does not require access to singular vectors of the target tensor unfolding and can be viewed as a black-box Tucker tensor algorithm. We employ DEIM-FS to reduce the computational cost associated with solving nonlinear tensor differential equations (TDEs) using dynamical low-rank approximation (DLRA). The computational cost of solving DLRA equations can become prohibitive when the exact rank of the right-hand side tensor is large. This issue arises in many TDEs, especially in cases involving non-polynomial nonlinearities, where the right-hand side tensor has full rank. This necessitates the storage and computation of tensors of size O(Nd). We show that DEIM-FS results in significant computational savings for DLRA by constructing a low-rank Tucker approximation of the right-hand side tensor on the fly. Another advantage of using DEIM-FS is to significantly simplify the implementation of DLRA equations, irrespective of the type of TDEs. We demonstrate the efficiency of the algorithm through several examples including solving high-dimensional partial differential equations.

Hyperpolarized 13 C metabolic imaging of the human abdomen with spatiotemporal denoising.

Improving the quality and maintaining the fidelity of large coverage abdominal hyperpolarized (HP) 13 C MRI studies with a patch based global-local higher-order singular value decomposition (GL-HOVSD) spatiotemporal denoising approach. Denoising performance was first evaluated using the simulated [1-13 C]pyruvate dynamics at different noise levels to determine optimal kglobal and klocal parameters. The GL-HOSVD spatiotemporal denoising method with the optimized parameters was then applied to two HP [1-13 C]pyruvate EPI abdominal human cohorts (n = 7 healthy volunteers and n = 8 pancreatic cancer patients). The parameterization of kglobal = 0.2 and klocal = 0.9 denoises abdominal HP data while retaining image fidelity when evaluated by RMSE. The kPX (conversion rate of pyruvate-to-metabolite, X = lactate or alanine) difference was shown to be <20% with respect to ground-truth metabolic conversion rates when there is adequate SNR (SNRAUC > 5) for downstream metabolites. In both human cohorts, there was a greater than nine-fold gain in peak [1-13 C]pyruvate, [1-13 C]lactate, and [1-13 C]alanine apparent SNRAUC . The improvement in metabolite SNR enabled a more robust quantification of kPL and kPA . After denoising, we observed a 2.1 ± 0.4 and 4.8 ± 2.5-fold increase in the number of voxels reliably fit across abdominal FOVs for kPL and kPA quantification maps. Spatiotemporal denoising greatly improves visualization of low SNR metabolites particularly [1-13 C]alanine and quantification of [1-13 C]pyruvate metabolism in large FOV HP 13 C MRI studies of the human abdomen.

Clutter filtering of angular domain data for contrast-free ultrafast microvascular imaging

Objective. Contrast-free microvascular imaging is clinically valuable for the assessment of physiological status and the early diagnosis of diseases. Effective clutter filtering is essential for microvascular visualization without contrast enhancement. Singular value decomposition (SVD)-based spatiotemporal filter has been widely used to suppress clutter. However, clinical real-time imaging relies on short ensembles (dozens of frames), which limits the implementation of SVD filtering due to the large error of eigen-correlated estimations and high dependence on optimal threshold when used in such ensembles. Approach. To address the above challenges of imaging in short ensembles, two optimized filters of angular domain data are proposed in this paper: grouped angle SVD (GA-SVD) and angular-coherence-based higher-order SVD (AC-HOSVD). GA-SVD applies SVD to the concatenation of all angular data to improve clutter rejection performance in short ensembles, while AC-HOSVD applies HOSVD to the angular data tensor and utilizes angular coherence in addition to spatial and temporal features for filtering. Feasible threshold selection strategies in each feature space are provided. The clutter rejection performance of the proposed filters and SVD was evaluated with Doppler phantom and in vivo studies at different cases. Moreover, the robustness of the filters was explored under wrong singular value threshold estimation, and their computational complexity was studied. Main results. Qualitative and quantitative results indicated that GA-SVD and AC-HOSVD can effectively improve clutter rejection performance in short ensembles, especially AC-HOSVD. Notably, the proposed methods using 20 frames had similar image quality to SVD using 100 frames. In vivo studies showed that compared to SVD, GA-SVD increased the signal-to-noise-ratio (SNR) by 6.03 dB on average, and AC-HOSVD increased the SNR by 8.93 dB on average. Furthermore, AC-HOSVD remained better power Doppler image quality under non-optimal thresholds, followed by GA-SVD. Significance. The proposed filters can greatly enhance contrast-free microvascular visualization in short ensembles and have potential for different clinical translations due to the performance differences.

A HOOI-Based Fast Parameter Estimation Algorithm in UCA-UCFO Framework.

In this paper, we introduce a Reduced-Dimension Multiple-Signal Classification (RD-MUSIC) technique via Higher-Order Orthogonal Iteration (HOOI), which facilitates the estimation of the target range and angle for Frequency-Diverse Array Multiple-Input-Multiple-Output (FDA-MIMO) radars in the unfolded coprime array with unfolded coprime frequency offsets (UCA-UCFO) structure. The received signal undergoes tensor decomposition by the HOOI algorithm to get the core and factor matrices, then the 2D spectral function is built. The Lagrange multiplier method is used to obtain a one-dimensional spectral function, reducing complexity for estimating the direction of arrival (DOA). The vector of the transmitter is obtained by the partial derivatives of the Lagrangian function, and its rotational invariance facilitates target range estimation. The method demonstrates improved operation speed and decreased computational complexity with respect to the classic Higher-Order Singular-Value Decomposition (HOSVD) technique, and its effectiveness and superiority are confirmed by numerical simulations.

Hybrid model of tensor sparse representation and total variation regularization for image denoising

The method based on non-local self-similarity patches has been widely applied in image denoising. For a given image patch, there are similar image patches at neighbor windows in the image. Traditionally, similar patches are vectorized and then rearranged into a matrix, which should have a low rank. Hence the denoising problem can be reformulated into a low rank recovery problem. However, the vectorization process can disrupt the spatial relationships among the patches. To improve this drawback, we rearrange the similar patches into a tensor to keep the spatial relationships. When the higher-order singular value decomposition (HOSVD) is applied to this tensor, the resulting core tensor should be sparse. In this paper, the sparse property of the core tensor is utilized to characterize similar patches, and then an optimization model is derived. Since the commonly used l0 norm regularization is NP-hard, we adopt the MCP function to constrain the sparse property of the core tensor. In addition, a total variation (TV) regularization term for the tensor is added to the model to preserve structural information in the image such as edges. Using the dual form to represent the total variation regularization and transforming the original problem into a saddle point problem, the primal–dual algorithm is applied to overcome the non-differentiability of the TV regularization. Finally, experimental results demonstrate that compared to existing denoising methods, the method proposed can better preserve details and structural information in the image.

Fast real-valued tensor decomposition framework for parameter estimation in FDA-MIMO radar

Frequency diversity array - Multiple input multiple output (FDA-MIMO) radar has a two-dimensional angle-range dependence due to the existence of certain frequency offset between transmitting elements. For obtaining angle-range estimation, a fast real-valued tensor propagator method (PM) for FDA-MIMO radar is developed. The developed approach is based on the real-valued tensor PM, which not only utilizes the original structural information of multidimensional information to improve estimation accuracy, but also eliminates the process of high-order singular value decomposition (HOSVD) on multidimensional data, greatly reducing computational complexity. Firstly, the unitary transformation technique is employed to convert the constructed tensor into a real-valued tensor. Next, construct a covariance tensor to obtain operator matrices in different directions. Then, a signal subspace is constructed using operator matrices. Finally, the selection matrices and the obtained signal subspace are employed to estimate angle and range information. The proposed algorithm can not only achieve parameter estimation at low snapshots, but also has much lower computational complexity than other algorithms at high snapshots. Therefore, the developed approach greatly reduces computational complexity while ensuring estimation accuracy, which enables it to be applied to massive FDA-MIMO radars. Simulation results confirm the accuracy advantage and high-efficiency of our algorithm.

Higher-order Singular Value Decomposition Filter for Contrast Echocardiography.

Assessing the coronary circulation with contrast-enhanced echocardiography has high clinical relevance. However, it is not being routinely performed in clinical practice because the current clinical tools generally could not provide adequate image quality. The contrast agent's visibility in the myocardium is generally poor, impaired by motion and non-linear propagation artifacts. The established multi-pulse contrast schemes (MPCS) and the more experimental singular value decomposition (SVD) filter also fall short to solve these issues. Here, we propose a scheme to process AM/AMPI echoes with higher-order singular value decomposition (HOSVD) instead of conventionally summing the complementary pulses. The echoes from the complementary pulses form a separate dimension in the HOSVD algorithm. Then, removing the ranks in that dimension with dominant coherent signals coming from tissue scattering would provide the contrast detection. We performed both in vitro and in vivo experiments to assess the performance of our proposed method in comparison with the current standard methods. A flow phantom study shows that HOSVD on AM pulsing exceeds the contrast-to-background ratio (CBR) of conventional AM and an SVD filter by 10dB and 14dB, respectively. In vivo porcine heart results also demonstrate that, compared to AM, HOSVD improves CBR in open-chest acquisition (up to 19dB) and contrast ratio in closed-chest acquisition (3dB).

A Higher-Order Singular Value Decomposition-Based Target Localization Algorithm for WiFi Array Systems

Traditional Angle of Arrival (AoA)-based WiFi array indoor localization algorithms do not fuse Channel State Information (CSI) inter-packet data for estimation, which makes WiFi arrays less effective for localization in complex indoor environments. Most algorithms are overburdened leading to inefficient localization. To address these issues, in this article, an indoor positioning algorithm based on Higher-Order Singular Value Decomposition (HOSVD) is proposed. First, the CSI data are reconstructed as a new measurement matrix by borrowing subcarriers, and a third-order tensor is constructed. Next, tensor compression techniques are used to reduce computational complexity and the signal subspace is obtained by HOSVD. Then, the AoA is obtained by the Reduced Dimension Multiple Signal Classification (RD-MUSIC) method. Finally, the coordinates of the target can be obtained by triangulating the AoAs of the three Access Points (APs). According to the simulation experiments, the AoA can be estimated accurately at a low SNR and with low snapshots. In practical experiments, we can successfully estimate the AoA in complex indoor environments with shorter timelines using HOSVD without modifications to commercial hardware and produce a lower AoA error and localization error rates compared to other algorithms. The effectiveness of our proposed algorithm is proven by simulations and practical experiments.

A novel grey prediction model based on tensor higher-order singular value decomposition and its application in short-term traffic flow

Short-term traffic flow prediction is the key to traffic guidance and control and can directly affect the performance of intelligent transportation systems. Traffic flow data has the characteristics of volatility, chaos, and randomness, which affect the accuracy of the prediction model. Based on the multi-dimensional spatio-temporal data characteristics of traffic flow data, this paper combines the tensor higher-order singular value decomposition theory and the modeling mechanism of the classical grey model GM(1,1) model and establishes the grey GM(1,1) model with tensor higher-order singular values. The tensor higher-order singular value decomposition reflects the periodic, multi-modal, and holistic nature of traffic flow data, which can mitigate the volatility and randomness of traffic flow data and improve the accuracy of the model. Then, the new model is applied to highway short-time traffic flow prediction, analyzing the spatio-temporal nature of traffic flow data, giving the detailed steps of model modeling, and analyzing the correlation between the original traffic flow data and tensor approximation data using grey correlation degrees. There are three cases to illustrate the effectiveness of the model. Case 1 shows that the results of MAPE from nine modeling objects are stable at about 5%, which indicates that the new model has some stability; Case 2 shows that the new model is more adaptable to short-time traffic flow prediction based on the results of three different modeling and prediction objects; Case 3 uses the new model to compare it with two traditional grey forecasting models and two optimization models, and the results indicate that the new model has a total MAPE value of 5.172%, which is better than the other four grey forecasting models. Finally, the new model is applied to short-time traffic flow prediction, and its prediction results are consistent with the trend of the original traffic flow data, indicating that it can reveal the real-time characteristics of the traffic system to a certain extent and provide a reliable theoretical basis for traffic planning, control, and optimization.

Solar Radiation and Weather Analysis of Meteorological Satellite Data by Tensor Decomposition

In this study, the data obtained from meteorological satellites were analyzed using tensor decomposition. The data used in this paper are meteorological image data observed by the Himawari-8 satellite and solar radiation data generated from Himawari Standard Data. First, we applied Higher-Order Singular Value Decomposition (HOSVD), a type of tensor decomposition, to the original image data and analyzed the features of the data, called the core tensor, obtained from the decomposition. As a result, it was found that the maximum value of the core tensor element is related to the cloud cover in the observed area. We then applied Multidimensional Principal Component Analysis (MPCA), an extension of principal component analysis computed using HOSVD, to the solar radiation data and analyzed the Principal Components (PC) obtained from MPCA. We also found that the PC with the highest contribution rate is related to the solar radiation in the entire observation area. The resulting PC score was compared to actual weather data. From the result, it was confirmed that the temporal transition of the amount of solar radiation in this area can be expressed almost correctly by using the PC score.

Smoothed Sparse Blind DOA Estimation for MC-CDMA Systems Based on Tensor Decomposition

We propose a blind direction of arrival (DOA) estimation method for multicarrier code-division multiple access (MC-CDMA) systems, which does not require knowledge of the spreading codes of transmitters. Our method involves reconstructing a fourth-order tensor with observations from the antenna array at the receiver. We then apply higher-order singular value decomposition (HOSVD) to separate the signal subspace from the noise subspace. To enhance the sparsity of the solution, we develop a smoothed ℓ0-norm sparse reconstruction method by designing continuous functions with reweighted vectors. Finally, DOA estimates are obtained by searching the spectrum of the sparse solution using an iterative method that ensures fast convergence. Numerical simulations show its superiority over previous work.

Using Neural Networks Algorithm in Ischemic Stroke Diagnosis: A Systematic Review.

To evaluate the evidence of artificial neural network (NNs) techniques in diagnosing ischemic stroke (IS) in adults. The Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) was utilized as a guideline for this review. PubMed, MEDLINE, Web of Science, and CINAHL Plus Full Text were searched to identify studies published between 2018 and 2022, reporting using NNs in IS diagnosis. The Critical Appraisal Checklist for Diagnostic Test Accuracy Studies was adopted to evaluate the included studies. Nine studies were included in this systematic review. Non-contrast computed tomography (NCCT) (n = 4 studies, 26.67%) and computed tomography angiography (CTA) (n = 4 studies, 26.67%) are among the most common features. Five algorithms were used in the included studies. Deep Convolutional Neural Networks (DCNNs) were commonly used for IS diagnosis (n = 3 studies, 33.33%). Other algorithms including three-dimensional convolutional neural networks (3D-CNNs) (n = 2 studies, 22.22%), two-stage deep convolutional neural networks (Two-stage DCNNs) (n = 2 studies, 22.22%), the local higher-order singular value decomposition denoising algorithm (GL-HOSVD) (n = 1 study, 11.11%), and a new deconvolution network model based on deep learning (AD-CNNnet) (n = 1 study, 11.11%) were also utilized for the diagnosis of IS. The number of studies ensuring the effectiveness of NNs algorithms in IS diagnosis has increased. Still, more feasibility and cost-effectiveness evaluations are needed to support the implementation of NNs in IS diagnosis in clinical settings.

Iterative refinement method by higher-order singular value decomposition for solving multi-linear systems

In this paper, the higher-order singular value decomposition and the LU decomposition are applied to solve the general multi-linear systems, rather than special structure like M−tensor. Here, we transform the general tensor system into a form with a special structure. In addition, an iterative refinement method is constructed by the information of the coefficient tensor itself, the higher-order singular value, instead of the spectra of iterative tensor. Finally, the numerical experimental results are given to demonstrate the efficiency of the iterative refinement method.

A user independent denoising method for x-nuclei MRI and MRS.

X-nuclei (also called non-proton MRI) MRI and spectroscopy are limited by the intrinsic low SNR as compared to conventional proton imaging. Clinical translation of x-nuclei examination warrants the need of a robust and versatile tool improving image quality for diagnostic use. In this work, we compare a novel denoising method with fewer inputs to the current state-of-the-art denoising method. Denoising approaches were compared on human acquisitions of sodium (23 Na) brain, deuterium (2 H) brain, carbon (13 C) heart and brain, and simulated dynamic hyperpolarized 13 C brain scans, with and without additional noise. The current state-of-the-art denoising method Global-local higher order singular value decomposition (GL-HOSVD) was compared to the few-input method tensor Marchenko-Pastur principal component analysis (tMPPCA). Noise-removal was quantified by residual distributions, and statistical analyses evaluated the differences in mean-square-error and Bland-Altman analysis to quantify agreement between original and denoised results of noise-added data. GL-HOSVD and tMPPCA showed similar performance for the variety of x-nuclei data analyzed in this work, with tMPPCA removing ˜5% more noise on average over GL-HOSVD. The mean ratio between noise-added and denoising reproducibility coefficients of the Bland-Altman analysis when compared to the original are also similar for the two methods with 3.09 ± 1.03 and 2.83 ± 0.79 for GL-HOSVD and tMPPCA, respectively. The strength of tMPPCA lies in the few-input approach, which generalizes well to different data sources. This makes the use of tMPPCA denoising a robust and versatile tool in x-nuclei imaging improvements and the preferred denoising method.